A review of orthogonal projections for calibration

Effective methods often rely on simple mathematical operators. Among these operators, orthogonal projections have been widely used because of their simplicity in compensating for detrimental factors. This efficiency depends largely on the way these tools are prepared. This article links the mathematical basics of orthogonal projections to the notion of vectoral subspaces, highlighting which information should be removed in the process and the important practical properties concerned with optimizing this technique. This review covers several methods involving orthogonal projections and focuses specifically on their practical use. This concerns the identification of detrimental information and its removal together with adjusting the dimension of the projection. The methodology discussed in this review will enable the reader to optimize orthogonal projections for any given situation. The concept and importance of orthogonal projections are presented and situated within pretreatments and calibrations. The key points of orthogonal projections are noted: identifying the right information, then building a basis of the subspace to remove detrimental information.